Supporting optimization of thick seam roadway with top coal based on orthogonal matrix analysis

Aiming at the problem of large deformation and difficulty in surrounding rock control of the top coal roadway in thick seam, theoretical analysis, theoretical analysis, numerical simulation, orthogonal matrix analysis and other methods were used to study the roof deformation and support parameter optimization of the top coal roadway in thick seam. Firstly, the structural model and roof mechanical model of the top coal roadway in thick seam were established, and the deformation coefficient TK was defined based on the relationship between curvature radius and bending moment, maximum bending moment and ultimate tensile strength of beam. According to the ratio of deformation rate between TK and beam to determine the roof deformation mode of top coal roadway, the discriminant conditions of roadway roof stability under two deformation conditions are obtained. Due to the characteristics of serious coal-rock fragmentation, large roof deformation, and integration of top coal and side coal. Therefore, the combined support method of “high prestressed long and short anchor cables” is proposed by double arch bearing structure control technology. Finally, based on the orthogonal matrix analysis method of supporting parameters optimization of the top coal roadway in thick seam, the analysis amount of supporting scheme is significantly reduced, the comprehensive evaluation of multi-factor and multi-supporting effect of roadway support is realized, and the optimal supporting scheme is obtained. Compared with the surrounding rock of the roadway without support, the deformation of the roof is reduced by 27.27%, the deformation of the two sides is reduced by 45.24%, and the tensile failure volume is reduced by 54.66%. The top coal roadway in thick seam has been effectively controlled, which provides guarantee for high yield and high efficiency of the mine.

www.nature.com/scientificreports/ arch composed of high prestressed anchor cables, which is a superposition and coupled support technology of large and small structures according to the failure characteristics of the soft rock composite roof. M. M. Murphy 20 studied the failure characteristics of different weak shale roofs and proposed corresponding control methods. Fu 21 proposed long and short anchor cable layer control technology for composite soft rock roadway. Wang 22 established a layered simplified mechanical model of coal roadway based on elastic foundation beam and essential layer theory. However, the above research did not qualitatively analyze the discriminant conditions of roof deformation and failure of supporting roof coal roadway and did not consider multi-factors and comprehensive evaluation of multi-support effects. Therefore, the deformation of the roadway and the optimization of supporting parameters for the top coal roadway in the thick seam have not been studied in depth. The above scholars have mainly studied the control of composite roof from two aspects of mining influence and mechanical properties of surrounding rock. However, the impact of mining is short-lived. This paper focuses on the optimization of rock support parameters for top coal roadways under specific surrounding rock geological conditions. In this paper, the structural model and the roof mechanics model of the top coal roadway in a thick seam are established. Based on the relationship between the radius of curvature and the bending moment of the beam, the maximum bending moment and the ultimate tensile strength of the beam, the determination conditions for the roof deformation mode of the roof-supporting coal roadway and the stability of the corresponding roadway roof are obtained. Based on the deformation and failure characteristics of the top coal roadway, the control technology of the double arch bearing structure with high prestressed long and short anchor cables is obtained. An orthogonal matrix analysis method for optimization of roadway support parameters in thick coal seam supporting top coal roadway is proposed, which significantly reduces the amount of analysis of support schemes and realizes comprehensive evaluation of multi-factor and multi-support effects of roadway support.

Surrounding rock deformation and control principle of the top coal roadway in thick seam
Mechanical model of roadway roof of the top coal roadway in thick seam. The average thickness of the mineable coal seam in Zhangcun Coal Mine is 5.69 m. Due to the large thickness of the coal seam, the great majority of the coal mine roadways are mainly supported roof coal roadways with top coal reserved along the bottom. When the thick coal seam is mined, the degree of coal fragmentation is severe, and the roof of the top-supporting coal roadway is challenging to control, which is prone to safety accidents. Based on the engineering geological background of Zhangcun Coal mine, the mechanical model of a thick coal seam supporting roadway roof is established. According to the field engineering problems, the following assumptions were made on the model to analyze its stability: (1) The coal and rock bodies at the roof of the roadway are considered beam A and beam B, which are homogeneous elastic structures. (2) An integrated structure is formed by beam A. The clamped beam C generates a bending moment under the horizontal force q 1 , as shown in Fig. 1a. (3) Under the action of the horizontal force q 1 , the clamped beam C will generate a bending moment between the beam B and the bottom floor, as shown in Fig. 1b. (4) The stiffness of beam A is greater than that of beam B, and beam A is the main load-bearing body. (5) There is a cohesive force between beam A and beam B, which both deform synergistically. In the actual strike length of transport roadway 2606, unit length was selected for study, and the beam structure of beam A and beam B with the fixed beam C as the fulcrum is shown in Fig. 2.
According to the previous study 23 , the relationship between the radius of curvature and the bending moment of the beam and the moment of inertia of the beam are expressed as follows: where q y is the load caused by the self-weight of beam A, kN/m; q m is the load caused by the self-weight of beam B, kN/m; q l is the uniform load generated in the horizontal direction, kN/m; q is the overlying load of beam A, kN/m. According to the above analysis, the deformation coefficient Tk between beams A and B is defined as follows 25 : When the beams A and B are under the combined effect of stress, the maximum tensile stress of the beam structure is 26 : where σ max is the ultimate tensile strength of the beam, MPa; σx is the horizontal stress of surrounding rock, MPa; W i is the bending section coefficient of beam, and its value is bh 2 /6 and M 3 .
When the sinking speed of beam A is lower than the sinking speed of beam B, the curvature radius ρ 1 of beam A is less than the radius of curvature ρ 2 of beam B, and the roof of the top coal roadway is deformed by layer separation. Simultaneous formulas (1), (2), (3) get the following relational formula: The compressive strength that the coal rock mass itself can bear is greater than the tensile strength. Therefore, the ultimate tensile strength of beams A and B is the condition for judging the stability of the roof. When the roof of the top coal roadway is deformed by delamination, the conditions for determining the stability of the roadway roof by combining formulas (2) and (4) are: When the subsidence rate ratio of beam B and beam A is less than the deformation coefficient, the top coal roadway will undergo large synergistic deformation. Simultaneous formulas (1), (2), (3) get the following relational formula: www.nature.com/scientificreports/ When the roof of the top coal roadway has a large collaborative deformation, the A beam and the B beam form a superimposed beam. At this time, the stability of the roof depends on the ultimate tensile strength of the B beam, and the judgment conditions for the stability of the roadway roof are: It can be seen from the above analysis that there are two main deformation and failure modes for the roof of the top coal roadway in thick seam. When the deformation between beam A and beam B satisfies Eq. (5), a large synergistic deformation occurs between them, as shown in Fig. 3a. Tensile failure occurs on the roof of the roadway. When the criterion (6) is exceeded, the roof deforms greatly, and the influence range is wide. Due to the large deformation of the roof, the anchor rod and the anchor cable were broken and failed. When the deformation of beam A and beam B satisfies Eq. (7), the delamination occurs between them, as shown in Fig. 3b. When the roadway roof exceeds the judgment condition (8), the separation and sliding between the rock layer and the coal seam occur, and the separation distance increases, resulting in shear deformation of the anchor rod and the anchor cable.
Combined control technology of long and short anchor cables on roof of top coal roadway in thick seam. For the top coal roadway in the thick seam, the roof support is significant for the stability of the entire roadway due to the integration of the top coal and the side coal. In summary, the support of the top coal roadway in thick seam should be considered: the high-strength support structure is adopted, and the high-strength support can carry the large coordinative deformation and delamination deformation of the roof. The high prestressed support structure is adopted. Due to the thick coal seam mining, the coal and rock mass is seriously broken, and the high prestressed support structure can carry out effective prestress diffusion and improve the stress state of the surrounding rock. Increase the scope of the anchorage area and improve the bearing capacity of the surrounding rock in the anchorage area. The top coal and the side coal are integrated, the principle of the same treatment of the top and the gang is adopted, and the roof and the gang part reinforcement is also considered. Therefore, the high prestressed long and short anchor cable double arch bearing structure is proposed to control the stability of the top coal roadway in the thick seam, as shown in Fig. 4.
According to Reference 27 , the bearing capacity of anchorage balanced arch is: where q is the bearing capacity of the arch, kN; D is the bolt or anchor cable spacing, m; Q is the bolt or anchor cable preload, kN; θ is internal friction angle of coal and rock mass, (°); l is the length of the bolt or anchor cable, m; R is the half the roadway span, m. According to Eq. (9), when the mechanical conditions of the roadway surrounding rock and the size of the roadway cross-section are specific, the anchor cable preload, length, and spacing are the main factors affecting

Numerical simulation analysis of the effect of high prestressed long and short anchor cable support of the top coal roadway in thick seam
Relying on the geological engineering background of the Zhangcun coal mine, a three-dimensional model with a size of 30 m × 15 m × 27 m (length × width × height) was constructed. The roadway is excavated along the 3# coal seam floor, and the cross-section of the roadway is rectangular, and the cross-sectional size is 5.8 m × 4 m (width × height). The Moore-Coulomb constitutive model was used for this simulation, and the model failure was consistent with the Moore-Coulomb failure criterion 28 . In order to simulate the actual geological environment, the surrounding and bottom surfaces of the model adopt normal displacement constraints, and the upper boundary is free and bears the uniform load acting on the boundary by the overlying rock. The upper boundary load of the model is 10 MPa, as shown in Fig. 5a. The lithological parameters used in the 3D model cover the range of literature 29,30 , as shown in Table 1. Long and short anchor cable supports are simulated by the built-in cable structural elements of FLAC 3D software 31 . The anchor cable structural element and the solid element are connected by link, rigid constraints are applied to the nodes, and pallets are simulated to realize the combined support of high prestressed long and short anchor cables in the roadway of the thick coal seam supporting the roof, as shown in Fig. 5b. The parameters used for the anchor cable are shown in Table 2. www.nature.com/scientificreports/ Support optimization orthogonal combination design. The stability of the roadway is controlled by the double arch bearing structure with high prestressed long and short anchor cables, but many parameters affect the support effect. Considering the support effect and economic cost, determining which parameters are the main factors affecting the stability of the surrounding rock is an essential link in the design of the support scheme. Therefore, the orthogonal experiment method can reduce the large number of experiments. According to the above formula (9), it can be seen that the three parameters of anchor cable prestress, anchor cable length, and anchor cable spacing are the main factors affecting the support effect. Under the premise of satisfying the factors and levels, a table of factors and levels is made, as shown in Table 3. In order to ensure the error analysis of the experiment, an empty column is set up, which is not listed in the table, and the L9(3 4 ) table is made according to the principle of orthogonal experimental design, as shown in Table 4. According to the orthogonal experimental design scheme, FLAC 3D software was used to obtain the orthogonal experimental range analysis, as shown in Table 5.

Support optimization orthogonal matrix analysis.
The evaluation of surrounding rock support effect is a comprehensive evaluation of multi-factor indicators, therefore a three-layer data model is constructed based on the above orthogonal experimental data 32 . The anchor cable prestress, length and spacing are used as the factor layers, and the top plate, the deformation of the two sides and the volume of the plastic zone are used as   www.nature.com/scientificreports/ the test evaluation index layers, as shown in Table 6. The weight matrix of each test evaluation index is obtained respectively, and then the weight matrix that affects the stability of the surrounding rock of the roadway is obtained, and finally the influence weight of different support parameters on the stability of the surrounding rock of the roadway is obtained.The process of solving each matrix is as follows 33 .
(1) Experiment evaluation index matrix: If there are l factors in the orthogonal experiment, and each factor has m levels, the average value of the experimental index at the j the level of factor A l is k ij . If the experimental evaluation index is as large as possible, then K ij = k ij , and the smaller the experimental evaluation index is, the better, then K ij = 1/k ij to establish a matrix (10).
(3) Horizontal layer matrix: the range of the factor A l in the orthogonal experiment is s i , (12) is established.
Since the smaller the deformation of the roadway roof, according to the experimental evaluation index weight matrix construction principle K ij = 1/k ij , combined with the data in Table 5, the roof evaluation index matrix M 1 is obtained as follows: The factor layer matrix T 1 can be obtained by formula (11) as follows: Combined with formula (12), the horizontal layer matrix S 1 can be obtained as shown below.
Similarly, the experimental evaluation index matrices M 2 and M 3 , the factor layer matrices T 2 and T 3 , and the horizontal layer matrices S 2 and S 3 are calculated. Combined with formula (13), the weight matrices w 1 , w 2 , and w 3 that affect the value of the experimental evaluation index can be obtained as follows.
Since the stability of the roadway cannot be controlled by a single factor, nor can it be investigated with a single index, it is necessary to obtain the total weight matrix of the three inspection indexes. By adding w 1 , w 2 , and w 3 to obtain the average value of the total weight matrix that affects the stability of the roadway 34,35 . It can be seen from matrix (18) that the optimal solution is A 2 B 3 C 1 , that is, the stability of the surrounding rock of the roadway is the best when the anchor cable prestress is 150KN, the anchor cable length is 4 m, and the anchor cable spacing is 0.9 m.     Figures 6,7,8,9, 10 and 11 are made by Origin 2018 software 36 and FLAC3D 6.0 software 37 . Figure 6 illustrates the deformation law of the two sides under different support schemes. In Fig. 6, the deformation law of two sides under the nine support schemes showed rapid deformation-slow deformation-stable deformation. When the support scheme is A 2 B 3 C 1 , the two sides reach the minimum deformation of stability. This is consistent with the results obtained from the orthogonal matrix.   Figure 7a,b show that the deformation on the two sides of the surrounding rock is divided into three developmental stages. When the surrounding rock is just excavated, the surrounding rock enters the stage of rapid deformation. When the surrounding rock excavation releases a part of the energy, the surrounding rock enters the slow deformation stage. The surrounding rock reaches a new equilibrium state, and the deformation of the surrounding rock tends to be stable. Figure 7a shows that when the surrounding rock is not supported, the deformation of the two sides of the surrounding rock reaches 52.6 mm. Figure 7b, when the optimal support scheme supports the surrounding rock, the deformation of the two sides of the surrounding rock reaches 28.8 mm, and the deformation of the two sides is reduced by 45.24%. Figure 8 illustrates the deformation law of the roof under different support schemes. In Fig. 8, the deformation law of roof under the nine support schemes showed rapid deformation-slow deformation-stable deformation. When the support scheme is A 2 B 3 C 1 , the roof reach the minimum deformation of stability. This is consistent with the results obtained from the orthogonal matrix. Figure 9 illustrates the comparison of the deformation of the surrounding rock roof under the unsupported and optimal support schemes. The monitoring points are arranged on the roof of the surrounding rock. The deformation law of the roof of the surrounding rock is obtained. Figure 9a,b show that the deformation of the surrounding rock roof is in three stages: rapid deformation, slow deformation, and tending to stability. It can be  www.nature.com/scientificreports/ seen from Fig. 9a that when the surrounding rock is not supported, the two sides of the surrounding rock reach 66 mm. In Fig. 9b, when the optimal support scheme supports the surrounding rock, the roof deformation of the surrounding rock reaches 48 mm, and the roof deformation is reduced by 27.27%. Figure 10 illustrates the volume variation law of the plastic zone under different support schemes. The failure volume of different states of the surrounding rock was extracted using the self-programmed FISH language. In Fig. 10, when the support scheme is A 2 B 3 C 1 , the total volume of the plastic zone is minimized. Compared with other support schemes, the volume of shear_past, shear_now, and tension_past of the surrounding rock under the group 6 support scheme is the smallest. From the nine support schemes, it can be seen that the surrounding rock is mainly dominated by shear_past. Figure 11 illustrates the volume comparison of the surrounding rock plastic zone under the unsupported and optimal support schemes. The plastic zone volume display program was written in the FISH language. The volume of shear_now, tension_now, shear_pas, and tension_past was obtained. Figure 11a shows that when the surrounding rock is not supported, the volume values of the four types of damage to the surrounding rock are 227.544, 7.36809, 511.379, and 95.7342, respectively. Figure 11b shows that when the optimal scheme supports the surrounding rock, the volume of the four types of damage to the surrounding rock are 218.453, 2.3168, 442.316, and 43.4006, respectively, decreasing by 3.99%, 67.9%, 13.5%, and 54.66%. After adopting the optimal support scheme, the failure volume values of tension_now and tension_past of the surrounding rock are significantly reduced. Based on the relationship between the radius of curvature and the bending moment of the beam, the maximum bending moment, and ultimate tensile strength of the beam, the deformation coefficient T K is defined. According to the ratio of deformation rate between T K and the beam, the deformation mode of the roof of the roadway supported by the top coal is judged, and the conditions for judging the stability of the roadway roof under the two deformation conditions are obtained. 2. Based on the deformation and failure characteristics of the top coal roadway in the thick seam, the coal and rock mass is severely broken, the roof is deformed greatly, and the top coal and the side coal are integrated, high prestressed long and short anchor cable double arch bearing structure control technology is proposed. 3. This paper proposes an orthogonal matrix analysis method for optimization of roadway support parameters in thick coal seam supporting top coal, which can significantly reduce the amount of support plan analysis, realize comprehensive evaluation of multi-factor and multi-support effects of roadway support, and obtain the optimal roadway support plan. Compared with the surrounding rock of the roadway without support, the deformation of the roof is reduced by 27.27%, the deformation of the two sides is reduced by 45.24%, and the tensile failure volume value is reduced by 54.66%. The top coal roadway in the thick coal seam has been effectively controlled, guaranteeing for the high production and high efficiency of the mine (Supplementary information S1).